Anomalous Skin Effect in Tin and Indium

Abstract

The normal-state reactive and resistive skin depths of very pure polycrystalline tin and indium have been measured as a function of frequency for frequencies between 7 and 20 000 cps. Measurements were made at liquid-helium temperatures, using specimens in the form of flat plates with a thickness of 1 mm. The free-electron anomalous-skin-effect theory of Reuter and Sondheimer was used to extrapolate the data to infinite frequency, and thus to obtain skin depths appropriate to the extreme anomalous limit. Analysis of the data based on the free-electron model and assuming diffuse electron scattering at the metal surfaces yields the values ${\left(\frac{\sigma }{l}\right)}_{\mathrm{Sn}}=(6.9\mathrm{}\pm 1.5)\times {10}^{10}$ ${\mathrm{\Omega }}^{-1\mathrm{}}$ ${\mathrm{cm}}^{-2\mathrm{}}$ and ${\left(\frac{\sigma }{l}\right)}_{\mathrm{In}}=(9.0\mathrm{}\pm 1.6)\times {10}^{10}$ ${\mathrm{\Omega }}^{-1\mathrm{}}$ ${\mathrm{cm}}^{-2\mathrm{}}$. The skin depths are estimated to deviate from their anomalous limits by approximately 2% at a frequency of 1 Mc/sec.